To find the value of , substitute into the equation . Plugging in gives us , which simplifies to . Now, add 15 to both sides: . Dividing both sides by -8, we find .

Now we have the solution .

Looking for similar equations, it’s interesting to note that linear equations can represent shadows of real-world scenarios. For example, in economics, they can model supply and demand, showing how one variable changes in response to another. Finding solutions can feel like solving mysteries—each point is a clue leading you to the bigger picture!

As for problem-solving, one common mistake is forgetting to correctly apply arithmetic signs while simplifying equations. Always double-check your signs, especially with negatives! It can save you from minor hiccups that lead to larger errors further into your problem-solving adventure.